Test #9, Section 4 (Calculator), #18

I’d be curious to hear what you think is the easiest way to solve Test #9, Section 4 (Calculator), #18. A lot of the students I work with find this challenging because the question says p percent (rather than using p as a decimal).

Thanks!

Which of the following equations describes a circle with radius 10 that passes through the origin when graphed in the xy-plane?

Which of the following equations describes a circle with radius 10 that passes through the origin when graphed in the xy-plane?

A) (x – 5)² + (y+5)² = 10

B) (x – 5)² + (y+5)² = 100

C) (x – 10)² + (y+10)² = 10

D) (x – 5√2)² + (y+5√2)² = 100

Clearly, A) is out because that one does not have a radius of 10. What is the most time-efficient way to solve this? Sketch and eyeball?

Can you explain this algebraically (even if you also give a graphed explanation)?

Can you explain this algebraically (even if you also give a graphed explanation)?

Radioactive substances decay over time. the mass M, in grams, of a particular radioactive substance d days after the beginning of an experiment is shown in the table below:

Number of days, d Mas, M (grams)
0 120.00
30 103.21
60 88.78
90 76.36

If this relationship is modeled by the function M(d) = a • 10^bd, which of the following could be the values of a and b?

A) a = 12 and b = 0.0145

B) a = 12 and b = -0.0145

C) a = 120 and b = 0.0022

D) a = 120 and b = -0.0022

College Board Test 4, Math 4 #25 (the explanation link that you previously made does not work)

College Board Test 4, Math 4 #25 (the explanation link that you previously made does not work):

f(x) = 2x^3 + 6 x^2 + 4x
g(x) = x^2 + 3x + 2

The polynomials f(x) and g(x) are defined above. Which of the following polynomials is divisible by 2x + 3?

A) h(x) = f(x) + g(x)

B) p(x) = f(x) + 3 g(x)

C) r(x) = 2 f(x) + 3 g(x)

D) s(x) = 3 f(x) + 2 g(x)

On SAT Practice Test 8, I got marked incorrect on Question 7 of the Math No-Calculator section.

On SAT Practice Test 8, I got marked incorrect on Question 7 of the Math No-Calculator section. This is because I said -1 is a valid solution when it isn’t supposed to be. However, if you plug in -1 into the original equation, and say that the square root of 4 is -2, the solution remains true.

So my question is, on the SAT, are you only ever supposed to use the principle square root of numbers? Saying that the square root of 4 = -2 is what rendered my answer incorrect.

On pg. 96 question 11

On pg. 96 question 11 I’m confused with how you came up with your answer even with the explanation. What am I supposed to do there?